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We consider the problem of estimating the mean vector $theta$ of a $d$-dimensional spherically symmetric distributed $X$ based on balanced loss functions of the forms: {bf (i)} $omega rho(|de-de_{0}|^{2}) +(1-omega)rho(|de - theta|^{2})$ and {bf (ii)} $ellleft(omega |de - de_{0}|^{2} +(1-omega)|de - theta|^{2}right)$, where $delta_0$ is a target estimator, and where $rho$ and $ell$ are increasing and concave functions. For $dgeq 4$ and the target estimator $delta_0(X)=X$, we provide Baranchik-type estimators that dominate $delta_0(X)=X$ and are minimax. The findings represent extensions of those of Marchand & Strawderman (cite{ms2020}) in two directions: {bf (a)} from scale mixture of normals to the spherical class of distributions with Lebesgue densities and {bf (b)} from completely monotone to concave $rho$ and $ell$.
Consider estimating the n by p matrix of means of an n by p matrix of independent normally distributed observations with constant variance, where the performance of an estimator is judged using a p by p matrix quadratic error loss function. A matrix
The James-Stein estimator is an estimator of the multivariate normal mean and dominates the maximum likelihood estimator (MLE) under squared error loss. The original work inspired great interest in developing shrinkage estimators for a variety of pro
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